The term computed tomography (CT) usually refers to processes whereby one or more images representing essentially any desired view of the internal structures of a physical object of interest are computed from a corresponding set of images representing respective geometric projections of the object.
To acquire the projection images of an object, a tomographic imaging apparatus requires: (i) a source of particles or electromagnetic radiation to probe the object, (ii) a detector to measure the resultant probe-object interactions, and (iii) a means for changing the relative orientation between the source/detector components and the object. The projection images constituting the image set thus represent measurements of the probe-object interactions acquired at respective relative orientations between the source/detector components and the object. These directions are typically chosen such that the source and detector follow a particular trajectory relative to the object, the trajectory depending on the geometry between the source and the detector. Examples of such trajectories include circular, helical and saddle trajectories.
Once the set of two-dimensional projection images at respective different relative orientations has been acquired, reconstruction algorithms are applied to these images to generate a corresponding data set referred to herein as a tomogram, representing the external and internal features of the object in three spatial dimensions. Using the tomogram as input, display software can then be used to visualise the object in essentially any way desired by a user, including as a rotating semi-transparent object, static and dynamic slices through the object along arbitrary directions, and the like. Such ‘reconstructed’ images are referred to herein as tomographic images.
X-ray computed-tomography (CT) enables non-destructive inspection of complex internal structures for a wide range of materials and length scales. It is a rapidly evolving technology which is readily finding new applications in fields such as biology, geology and materials science. CT systems capable of producing CT images of micron-scale features are referred to in the art as micro-CT systems. Current state-of-the-art lab-based micro-CT systems typically spend 8-12 hours acquiring x-ray projection data of a sample or object of interest in order to produce a high-quality tomogram containing 20483 voxels, with voxel side-lengths of 2-3 microns.
However, in many applications, the features of interest are too small to be clearly resolved in micro-CT images with this spatial resolution. For example, FIG. 1 compares a micro-CT image slice (left-hand image) from a tomogram with a 2.5 μm voxel (edge) size with a scanning electron microscope (SEM) image (right-hand image) with a 0.7 μm pixel dimension of the same region. The open regions of the sample visible in the SEM image are not clearly resolved in the micro-CT image, precluding use of the latter for accurate quantitative analysis of the sample porosity. As discussed below, the spatial resolution of micro-CT can be improved at the expense of significantly longer acquisition times. However, longer acquisition times increase the per-image cost and decrease throughput, which are generally undesirable for micro-CT systems in commercial environments.
Achieving increased resolution while maintaining acceptable acquisition times is a major challenge for lab-based cone-beam micro-CT systems. For resolutions at or below the micron scale, existing CT systems and methods require prolonged acquisition times to keep the signal-to-noise ratio (SNR) from compromising image fidelity. However, reduced acquisition times would improve specimen throughput, thereby increasing the appeal of micro-CT imaging in a range of commercial applications.
High-Resolution Imaging and Signal-to-Noise Ratio
A major obstacle when increasing the image resolution of lab-based cone-beam micro-CT systems is the relationship between radiographic resolution, X-ray source spot size, and projection data signal-to-noise ratio (SNR). Due to penumbra effects, the lower limit to radiographic resolution is the X-ray source spot diameter; however, X-ray flux is roughly proportional to source spot area. Therefore, in order to increase the resolution by a factor of 2, one must decrease the source spot area, and consequently the X-ray flux, by a factor of 4. The dominant contribution to image noise in a properly configured (i.e., quantum limited) detector is shot noise (i.e., statistical noise) arising from finite photon numbers. The projection data SNR scales with the square root of the number of X-ray photons detected at each pixel of the detector. Consequently, to maintain a given SNR and double the resolution, the acquisition time must be 4 times longer. At high resolutions, this square-law relationship leads to unacceptably long acquisition times, and high resolution imaging also places stringent stability requirements on system components.
X-ray tubes generally produce a near-isotropic x-ray beam flux over a solid angle of almost 2π steradians. The simplest way to alleviate the diminishing SNR is to move the detector closer to the source, thereby capturing a larger proportion of the X-ray beam.
However, this means operating the imaging system at a high cone-angle, as will be apparent from the system geometry shown in FIG. 2.
Data Sufficiency
As described above, tomograms and tomographic images are not acquired directly, but are reconstructed from a set of acquired projection images of the specimen. The X-ray source and detector (or equivalently: the sample) move along a predetermined trajectory, so that each projection image is collected at a different projection angle. The algorithm used to reconstruct a tomogram depends largely on the trajectory used for collecting the projections.
In order to reconstruct an accurate tomogram or tomographic image, the acquired projection data should contain complete information about the object. Data completeness for 3D tomography was first addressed by Tuy (see H. K. Tuy, “An inverse formula for cone-beam reconstruction,” SIAM J Appl. Math, vol. 43, pp. 546-552, 1983). Tuy formulated a general criterion for acquisition trajectories which guarantees that complete information can be collected. A trajectory that satisfies this criterion is referred to in the art as a complete trajectory. However, it will be understood by those skilled in the art that the completeness of a trajectory is dependent upon the tomographic volume that is reconstructed. Consequently, in this specification the term complete trajectory is defined as one that satisfies the Tuy criterion for at least a substantial fraction of the reconstructed tomogram.
A single closed circle trajectory does not provide complete data for 3D reconstruction. Regardless of sampling density, data collected along such a trajectory does not contain all the information needed to reconstruct the object, and consequently only an approximate reconstruction is possible. As long as the cone-angle is small, acquiring projection data along a circle trajectory is almost complete (e.g., a cone-angle of <5° is typically acceptable). However, the amount of missing data increases as the cone-angle increases.
A complete trajectory can be obtained by appending to the circle a line segment perpendicular to the circle plane. Other such complete trajectories include a helix, and a saddle. Projection data collected along these (and other complete) trajectories provide sufficient information for (theoretically) exact reconstruction. Indeed, theoretically-exact reconstruction algorithms have been known for some time. Although exact reconstruction is not achieved in practice due to factors such as noise and finite sampling, it is nevertheless desirable to use theoretically-exact reconstruction methods in order to remove systematic errors in the reconstruction due to approximations in the underlying inversion formula.
Using a complete trajectory, in principle a tomographic imaging apparatus can operate at an arbitrarily large cone-angle, opening up the possibility of moving the detector as close to the source as physically possible. With the added benefit of being able to image objects of arbitrary height, the helix is of particular interest. A number of known reconstruction methods are able to generate tomograms from projection data acquired along a helical trajectory, including approximate iterative methods such as the Algebraic Reconstruction Technique (ART) and the Simultaneous Iterative Reconstruction Technique (SIRT), and filtered backprojection-type reconstruction methods based on the theoretically-exact Katsevich 1PI inversion formula, or helix variants of the approximate Feldkamp-Davis-Kress (FDK) reconstruction method.
Several existing types of CT systems can achieve (sub)micrometer resolution. For example, ultra-fine-focus systems utilise scanning electron microscopes (SEM) for X-ray generation. However, these can only produce X-rays up to about 30 kV, and are limited to sub-millimeter specimen diameter. Furthermore, since the specimen is placed in a vacuum chamber, they cannot easily accommodate experimental rigs.
X-ray lens based systems use a condenser lens to increase X-ray flux from the source. These systems are also limited to low X-ray energies due to the high aspect ratios required in the Fresnel zone plates for hard X-rays. Good resolution is obtained by using very small detector elements, mandating a very thin scintillator. As a result, only a small fraction of the X-ray photons are detected, leading to long acquisition times despite the relatively high X-ray flux in these systems.
Fine focus systems are a third alternative. Like ultra-fine-focus systems, they do not rely on X-ray optics, but offer much greater flexibility both in the range of X-ray energies which can be used—and as a consequence what objects can be imaged—since no vacuum chamber is needed. Furthermore, the propagation path between the X-ray source and the detector is completely open, making such systems ideally suited when auxiliary experimental rigs are required.
A fourth configuration type is the quasi parallel configuration, in which the sample is placed closer to the detector than the source, giving a geometric magnification close to 1. This geometry enables a much higher radiographic resolution for a given source spot size than the fine focus configuration, allowing the use of sources with a much higher flux. However, the larger source-sample distance mandates the use of a smaller cone angle, meaning that in practice the x-ray flux incident on the sample is not improved dramatically. Secondly, at high resolution a thin scintillator must be used, resulting in a very low X-ray detection efficiency, typically less than 5%, compared to over 60% for modern large flat-panel detectors.
The following discussion deals exclusively with the fine-focus system type.
Conventional fine-focus micro-CT systems are lens-free fine-focus configurations that use a circular trajectory, and reconstruction is performed with the Feldkamp-Davis-Kress (FDK) algorithm. This offers great simplicity and reliability, as it requires only a single rotation stage. As described above, however, collecting projection data along a circular trajectory does not provide complete information about the object, and is not suited for imaging with x-ray beam cone-angles beyond 5°. Consequently, to obtain an acceptable SNR, long acquisition times are used. These same limitations apply to circular trajectory ultrafine-focus systems which utilise scanning electron microscopes (SEM) for X-ray generation.
The commercial helical micro-CT system manufactured by SkyScan uses a fine-focus helical trajectory and FDK reconstruction. As described above, the helical trajectory is complete. However, the approximate nature of the FDK reconstruction algorithm means that data acquisition can only be performed with a moderate or small helix pitch, necessitating long acquisition times when scanning a long object.
In principle, reconstruction methods based on exact inversion formulas can be used to perform tomographic imaging at arbitrarily high cone-angle, and are therefore not limited to a small pitch. However, the inventors have identified that, at high pitch, the inherent asymmetry of the helix trajectory implies that the acquired set of projections represents an uneven spatial sampling of the imaged object. This leads to tomograms with substantially non-uniform spatial resolution, and therefore reduced utility.
It is desired to provide a computed tomography imaging process and system that alleviate one or more difficulties of the prior art, or that at least provide a useful alternative.